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On May 31, 2020 a convective storm appeared in one small cyclone in the South Temperate Belt (STB) of Jupiter. The storm, nicknamed as Clyde's Spot, had an explosive start and quickly diminished in activity in a few days. However, it left a highly turbulent cyclone as a remnant that evolved to become a turbulent segment of the STB in a time-scale of one year. A very similar storm erupted on August 7, 2021 in another cyclone of the STB with a similar initial phenomenology. In both cases, the outbreaks started in cyclones that were the result of the merger of pre-existing vortices. In a previous paper we presented an observational study of these storms compared with a similar cyclonic convective system observed during the Voyager 2 flyby [Hueso et al., Convective storms in closed cyclones in Jupiter's South Temperate Belt: (I) Observations, Icarus, 380, 2022]. Here we present numerical simulations of these vortices and storms with the Explicit Planetary Isentropic-Coordinate (EPIC) numerical model. We simulate mergers of cyclones in Jupiter's STB and investigate the deep structure of the resulting cyclone and its capability to uplift material from the water condensation level. Convection is introduced in the model imposing heating sources whose vertical extent, horizontal size and duration are free parameters that we explore. Our simulations reproduce the cloud field of both storms after short episodes of a few hours of intense con-vection. The evolution of the morphology of the convective cyclone after the convective pulse stopped shows a strong relation between the convective energy released and the initial vorticity in the cyclone. Similar results are obtained for the cyclonic storm observed during the Voyager 2 flyby. We also compare our simulations of these storms with numerical simulations of a storm that developed in the STB in 2018 inside an elongated cyclone known as the South Temperate Belt Ghost [Inurrigarro et al., Observations and numerical modelling of a convective disturbance in a large-scale cyclone in Jupiter's South Temperate Belt, Icarus, 336, 2020]. In addition, we also simulate one of the large-scale storms that develop in the South Equatorial Belt comparing our simulations with Voyager 1 observations of one of those events. From these simulations, we establish a relative scale of energies associated to these convective storms. As coherent cyclones isolate the local atmosphere from their surroundings, we propose that the availability of condensables inside closed cyclones limits the duration of active convection, allowing larger convective outbursts in larger cyclones. Our simulations of the short and intense convective pulse associated to the 2020 and 2021 STB suggest a minimum local water abundance of 1.0-1.2 times solar at the location of the storms. The lower number considers a significant contribution of ammonia condensation, and the larger number considers only water moist convection with a negligible role of ammonia. This work has been supported by Grant PID2019-109467GB-I00 funded by MCIN/AEI/10.13039/501100011033/ and by Grupos Gobierno Vasco IT1366-19. PI acknowledges a PhD scholarship from Gobierno Vasco.